A Unified Gas-kinetic Particle Method for Multiscale Photon Transport

TL;DR

This paper introduces a unified gas-kinetic particle method that accurately simulates multiscale photon transport across different regimes, improving computational efficiency and avoiding common discretization issues.

Contribution

The proposed UGKP method unifies transport physics modeling in a single framework, capturing diffusive, free transport, and transition regimes without velocity space discretization.

Findings

Accurately models all transport regimes from optically thin to thick.

Recovers diffusion solutions with large cell sizes and time steps.

Avoids ray effects common in discrete ordinate methods.

Abstract

In this work, we present a unified gas-kinetic particle (UGKP) method for the simulation of multiscale photon transport. The multiscale nature of the particle method mainly comes from the recovery of the time evolution flux function in the unified gas-kinetic scheme (UGKS) through a coupled dynamic process of particle transport and collision. This practice improves the original operator splitting approach in the Monte Carlo method, such as the separated treatment of particle transport and collision. As a result, with the variation of the ratio between numerical time step and local photon's collision time, different transport physics can be fully captured in a single computation. In the diffusive limit, the UGKP method could recover the solution of the diffusion equation with the cell size and time step being much larger than the photon's mean free path and the mean collision time. In the free transport limit, it presents an exact particle tracking process as the original Monte Carlo method. In the transition regime, the weights of particle free transport and collision are determined by the ratio of local numerical time step to the photon's collision time. Several one-dimensional numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the current scheme. In comparison with the $S_N$ discrete ordinate method, the UGKP method is based on particles and avoids the discretization of particle velocity space, which does not suffer from the ray effect.